In this page we have NCERT Solutions for Square roots Class 8 Maths Chapter 6 for
EXERCISE 6.2 . Hope you like them and do not forget to like , social share
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Question 1
Find the square of the following numbers.
(i) 32
(ii) 35
(iii) 86
(iv) 93
(v) 71
(vi) 46
Answer
(i) 32
2
We can find the square using direct multiplication
= 32 x 32 = 1024
But above method can be cumbersome to calculate. We can calculate such values in the another better way f
Since, 32 can be written as (30+2)
So, 32
2 = (30+2)
2 = (30+2)(30+2)
Now we know the identity
(a+b)
2= a
2 + b
2 +2ab
= 30
2 + 2 x 30 x 2 + 2
2
= 900 + 120 + 4 = 1024
(ii) (35)
2 = (30+5)
2
Solving on similar lines as above
= 30
2 + 2 x 30 x 5 + 5
2
= 900 + 300 + 25 = 1225
(iii) 86
2 = (80 + 6)
2
= 80
2 + 2 x 80 x 6 + 6
2
= 6400 + 960 + 36 = 7396
(iv) 93
2 = (90+3)
2
= 90
2 +2 x 90 x 3 + 3
2
= 8100 + 540 + 9 = 8649
(v) 71
2 = (70 + 1)
2
= 70
2 +2 x 70 x 1 + 1 x 1
= 4900 + 140 + 1 = 5040 + 1 = 5041
(vi) 46
2 = (40+6)
2
= 40
2 + 2 x 40 x 6 + 6
2
= 1600 + 480 + 36 = 2080 + 36 = 2116
Question 2
Write a Pythagorean triplet whose one member is:
(i) 6
(ii) 14
(iii) 16
(iv) 18
Answer
As we know 2n, n
2 + 1 and n
2 - 1 form a Pythagorean triplet for any number, n > 1.
(i) If we take n
2 + 1 or n
2 - 1 to be 6 then then the value of n will not integer(n
2 will be 5 or 7)
So we can 2n = 6
Therefore, n = 3
And, n
2 + 1 = 3
2 + 1= 9 + 1 = 10
And,n
2 - 1 = 3
2 - 1 = 9 - 1 = 8
Test: 6
2 + 8
2 = 36 + 64 = 100 = 10
2
Hence, the triplet is 6, 8, and 10 Answer
(ii) If we take n
2 + 1 or n
2 - 1 to be 14 then then the value of n will not integer(n
2 will be 15 or 13)
So we can take 2n= 14, therefore, n = 7
Now, n
2 + 1 = 7
2 + 1 = 49 + 1 = 50
And, n
2 - 1 = 7
2 - 1 = 49 - 1 = 48
Test: 14
2 + 48
2 = 196 + 1304 = 2500 = 50
2
Hence, the triplet is 14, 48, and 50 Answer
(iii) If we take n
2 + 1 or n
2 - 1 to be 16 then then the value of n will not integer(n
2 will be 17 or 15)
Let us assume 2n = 16, then n = 8
Now, n
2 + 1 = 8
2 + 1 = 64 + 1 = 65
And, n
2 - 1 = 8
2 - 1 = 64 - 1 = 63
Test: 16
2 + 63
2 = 256 + 3969 = 4225 = 65
2
Hence, the triplet is 16, 63, and 65 Answer
(iv) If we take n
2 + 1 or n
2 - 1 to be 18 then then the value of n will not integer(n
2 will be 19 or 17)
Let us assume 2n = 18, therefore, n = 9
Now, n
2 + 1 = 9
2 + 1 = 81 + 1 = 82
And, n
2 - 1 = 9
2 - 1 = 81 - 1 = 80
Test: 18
2 + 80
2 = 324 + 6400 = 6724 = 82
2
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